No abstract

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment of stock, this shipment will be delivered in a fixed or perhaps random length of time, but at any rate with a time lag which is independent of the size of the order placed. There are, however, a number of situations met in practice in which this assumption is not a tenable one. An important example arises when there are several installations, say 1, 2, ..., N, with installation 1 receiving stock from 2, with 2 receiving stock from 3, etc. In this example, if an order is placed by installation 1 for stock from installation 2, the length of time for delivery of this stock is determined not only by the natural lead time between these two sites, but also by the availability of stock at the second installation. In this paper we shall consider the problem of determining optimal purchasing quantities in a multi-installation model of this type.

Hairy vetch (Vicia villosa Roth) fixes N for corn (Zea mays L.) production, and cereal rye (Secale cereale L.) accumulates soil N to reduce potential N losses. The objective of this research was to identify optimum seeding rates of vetch‐rye cover crop mixtures at Coastal Plain and Piedmont locations in Maryland. Mixtures evaluated were 14, 21, and 28 kg vetch ha−1, and 47 or 94 kg rye ha−1 in complete factorial combination. Pure vetch, rye, and no cover crop were used as controls. Cover crops were killed in early April (early kill) and early May (late kill), followed by no‐till corn without fertilizer N. Corn grain yields were significantly higher following late‐killed covers. Coastal Plain grain yields ranged from 3.1 to 7.0 Mg ha−1 and Piedmont yields ranged from 5.2 to 10.7 Mg ha−1. Within each kill date, corn yield was highest following vetch, lowest following rye, and intermediate following all six mixtures. Cover crop yield increased by 160% in the Piedmont and 83% at the Coastal Plain location when kill was delayed. Except for pure rye, N content was 1.6 to 2 times greater by the late kill date. Total N content was equal for all vetch‐rye mixtures at each date and within location, ranging from 74 to 109 kg ha−1 for early kill, and from 136 to 219 kg ha−1 for late kill. Carbon‐to‐nitrogen ratios (C/N) were 25:1 for all mixture combinations at the Piedmont location and for mixtures with low rye component at the Coastal Plain location. The best seeding rate mixture for corn production was 21 kg vetch ha−1 and 47 kg rye ha−1. The vetch‐rye mixture can scavenge potentially leachable N, while maintaining corn yields by adding fixed N to the cropping system.

Spring kill date affects cover crop N content and N availability to subsequent no‐till corn (Zea mays L.). This 2‐yr study was conducted in 1990 and 1991 at Coastal Plain and Piedmont locations in Maryland to evaluate three cover crop kill dates, three corn planting dates, and four corn fertilizer N (FN) rates following hairy vetch (Vicia villosa Roth), cereal rye (Secale cereale L.) and a vetch‐rye mixture. No‐cover checks were included for each corn planting date. Fertilizer N rates were 0 to 202 kg ha−1 in the Piedmont and 0 to 270 kg ha−1 for the Coastal Plain. The vetch‐rye mixture contained as much or more N than vetch, and more N than rye within each kill date. Cover crop biomass and N content increased for each delay in kill. In a 50‐d period from late March until early May, vetch and the vetch‐rye mixture accumulated about 2 kg N ha−1 d−1, with total topgrowth N accumulation from 144 to 203 kg ha−1 over two locations and two years. Greatest rye N accumulation was 51 kg ha−1. Corn N content ranged from 37 to 293 kg ha−1, and was significantly affected by FN rate. Within FN rate, N content was greater following vetch or vetch‐rye than following rye or no cover, particularly at low FN rates. Corn N content was greater if cover kill and corn planting were delayed until late April or mid‐May. This was attributed to greater cover crop N production and mulching effects, and the timing of summer rainfall. Corn FN requirements were greatest following rye or no cover, intermediate following vetch‐rye, and least following vetch. This demonstrates that cover crop species and kill date can be managed to conserve N with rye, supply N for the next crop with vetch, or provide both N conservation and N supply with a vetch‐rye mixture.

Winter cover crops can supply N to the next crop, reduce erosion and N leaching, and conserve or deplete soil moisture. To identify optimum corn fertilizer nitrogen (FN) rates following cover crops, we evaluated hairy vetch (Vf: Jlicia villosa Roth), Austrian winter pea [PE: Pisum sativum L. subsp. sativum var. arvense (L.) Poir.], crimson clover (CR: Trifolium incartUllum L.), and wheat (WH: Triticum aes· ti~·um L.) winter cover crops in the U.S. Coastal Plain and Piedmont for no-tillage corn (Zea mays L.) at four FN rates (topdressed NH 4 N0 3 ) onr 4 yr. Parameters evaluated included cover crop yield and N content, corn N uptake, and corn grain yield. On the Coastal Plain, Vf, PE, CR, and WH topgrowth averaged 205, 180, 170, and 40 kg N ha-•, respectively, and ~40% less for the Piedmont. With no FN, grain yields were generally greater after legumes than after no cover crop, and lowest after WH, with the best yields after legumes with 90 to 135 kg FN ha-•. Synergistic responses occurred when FN was ap· plied after legumes. Non·N-Iimited grain yield increases averaged 2 Mg ha-• (Coastal Plain) and 0.5 Mg ha-• (Piedmont), and were not directly related to cover crop N. With no cover crop, FN needed for maximum yield averaged 80 kg ha -• (Piedmont) and 135 kg ha -• (Coastal Plain). After WH, FN needs increased 15 to 30 kg ha-•, but decreased 10 to 75 kg ha-• after legumes. Hairy vetch provided the most consistent increases, with average grain yield of 10.6 Mg ha-1 (Coastal Plain) and 8.2 Mg ha-1 (Piedmont), and an economic opti· mum FN rate of 127 (Coastal Plain) and 66 kg ha-• (Piedmont).